Yaujen Wang

We previously introduced the concepts of optical centroid efficiency (OCE) and enclosed energy within a rectangular pixel (EOD). We applied them to an ideal lens with and without a central obscuration for two different detector pixel sizes. Also, we analyzed the performance of OCE vs. EOD for the following three Seidel primary aberrations of an ideal lens: spherical, coma, and astigmatism, plus defocus. In this paper, we concentrate on three different optical remote sensing instrument configurations. We burden them with a set of aberrations to mimic realistic generalized error budgets that cover potential ground, lunch, and on-orbit environmental conditions. The shape of the OCE vs. EOD curve depends to a large degree on the dominant aberration. With the proper choice of detector pixel size, OCE increases with EOD when EOD is larger than 0.6. The increased detector pixel size is advantageous for structures that enhance diffraction effects, and for off-axis and asymmetrical configurations. Analytical and experimental tests are proposed for original critical cases. Furthermore, OCE and EOD, as functional figures of merit, may be effectively applied to instruments for monitoring tumors and their evolution to cancerous tissue, leading to timely diagnosis.

We previously proposed that the optical centroid efficiency (OCE) might be a preferred figure-of-merit to the enclosed energy of a rectangular pixel (EOD) for an instrument subject to unpredictable environmental jitter and alignment conditions. Here we follow the same symbols for the corresponding quantities, particularly the width of the pixel as being equal to 2d. Here we analyze the performance of the OCE vs. the EOD for the three Seidel primary aberrations of an optical component: spherical, coma, and astigmatism, plus defocus. We show that the OCE has an approximate U-shape when graphed against the EOD, for the aberrations ranging from 0 to 1.25λ. We conclude that for pixels larger than 2d = 3λF/#, a small pixel will feature better performance when expecting jitter, misalignment, and other environmental and unpredictable conditions. When evaluating the performance of low-aberration instruments in dynamic and unpredictable environments, the choice of the lager pixel 2d = 7λF/# might be advantageous. Its selection will result in the deterioration of image resolution.

The noise-equivalent power is used to predict performance of infrared (IR) sensors. In a general IR or remote sensing system, the axes of the incoming chief ray of each pixel in the optical system and the center of that detector pixel are slightly misaligned, due to optical tolerances, jitter, and other environmental conditions, leading to error in the sensor performance prediction and estimates. A new figure-of-merit, the optical centroid efficiency (OCE), considers the energy on the rectangular detector pixel, averaged over all positions on the pixel. We calculate the OCE as a function of energy on detector (EOD) for a popular IR imaging system, a three-mirror reflector.

Optical centroid efficiency (OCE) is the traditional enclosed energy by the square detector pixel (the energy on detector (EOD)) averaged over all misalignments between the optical system and the pixel center. We examine the relationship between the OCE and the EOD for two different pixel sizes, with one larger than the diameter of the Airy disc and the other smaller than three diameters of the Airy disc. We observed that the relationships could, in general, be described as having a U shape, with the OCE being proportional to the EOD for small amounts of aberrations and inversely proportional for large amounts. For the letter cases, the energy is distributed over several pixels.

The off-axis three-mirror optical system is derived from the classical Cooke triplet or a derivative of the inverse-telephoto lens. By properly arranging an internal reimaging mechanism or altering the location of the optical stop, one can create different versions of three-mirror optical systems. They include very compact configurations and wide field-of-view imagers. Insights into the optical design process, manufacturing, stray light management, and remote sensing applications are presented.

High-performance megapixel focal plane arrays with small pixels have been widely used in modern optical remote sensing, astronomical, and surveillance instruments. In the prediction models applied in the traditional instrument performance analysis, the image of a point source is assumed to fall on the center of a detector pixel. A geometrical image of a point source in the realistic optical system may actually fall on any position on the detector pixel because the sensor’s line of sight includes pointing errors and jitter. This traditional assumption may lead to an optimistic error, estimated at between 10% and 20%. We present the critical factors that impact the performance estimate in a realistic instrument design based on the prediction for the noise-equivalent power (NEP). They are the optical centroid efficiency (OCE) and the ensquared energy, or more precisely, the energy on the rectangular detector pixel (EOD). We performed the simulation studies for imaging with an optical system with and without a generalized rectangular central obscuration.